Question

A bullet is fired into the air at an angle of 45°. How far does it travel before it is 1,000 feet above the ground? (Assume that the bullet travels in a straight line; neglect the forces of gravity, and give your answer to the nearest foot.)

Answer 1

Answer:

It travels 1414 feets.

Explanation:

Let's take the length the bullet travels l as the hypotenuse of a right triangle and the height it reaches one of its sides. Since we got the angle α at which it was fired and the height h it reached, we can calculate l using the sin(α) function:

$sin(\alpha )=\frac{opposite side}{hypotenuse}\\sin(\alpha)=\frac{h}{l}\\l=\frac{h}{sin(\alpha)}$

Replacing:

$l=\frac{1000ft}{sin(\frac{\pi}{4})}$

Solving and roundin to the nearest foot:

$l=1414 ft$